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Interareal connectomes are whole-brain wiring diagrams of white-matter pathways. Recent studies have identified modules, hubs, module hierarchies and rich clubs as structural hallmarks of these wiring diagrams. An influential current theory postulates that connectome modules are adequately explained by evolutionary pressures for wiring economy, but that the other hallmarks are not explained by such pressures and are therefore less trivial. Here, we use constraint network models to test these postulates in current gold-standard vertebrate and invertebrate interareal-connectome reconstructions. We show that empirical wiring-cost constraints inadequately explain connectome module organization, and that simultaneous module and hub constraints induce the structural byproducts of hierarchies and rich clubs. These byproducts, known as spandrels in evolutionary biology, include the structural substrate of the default-mode network. Our results imply that currently standard connectome characterizations are based on circular analyses or double dipping, and we emphasize an integrative approach to future connectome analyses for avoiding such pitfalls. Whole-brain networks of long-range neuronal pathways are characterized by interdependencies between structural features. Here the author shows that module hierarchy and rich club features in these networks are structural byproducts (spandrels) of module and hub constraints, but not of wiring-cost constraints.

Brain connectivity datasets comprise networks of brain regions connected by anatomical tracts or by functional associations. Complex network analysis—a new multidisciplinary approach to the study of complex systems—aims to characterize these brain networks with a small number of neurobiologically meaningful and easily computable measures. In this article, we discuss construction of brain networks from connectivity data and describe the most commonly used network measures of structural and functional connectivity. We describe measures that variously detect functional integration and segregation, quantify centrality of individual brain regions or pathways, characterize patterns of local anatomical circuitry, and test resilience of networks to insult. We discuss the issues surrounding comparison of structural and functional network connectivity, as well as comparison of networks across subjects. Finally, we describe a Matlab toolbox (http://www.brain-connectivity-toolbox.net) accompanying this article and containing a collection of complex network measures and large-scale neuroanatomical connectivity datasets.

Complex functional brain networks are large networks of brain regions and functional brain connections. Statistical characterizations of these networks aim to quantify global and local properties of brain activity with a small number of network measures. Important functional network measures include measures of modularity (measures of the goodness with which a network is optimally partitioned into functional subgroups) and measures of centrality (measures of the functional influence of individual brain regions). Characterizations of functional networks are increasing in popularity, but are associated with several important methodological problems. These problems include the inability to characterize densely connected and weighted functional networks, the neglect of degenerate topologically distinct high-modularity partitions of these networks, and the absence of a network null model for testing hypotheses of association between observed nontrivial network properties and simple weighted connectivity properties. In this study we describe a set of methods to overcome these problems. Specifically, we generalize measures of modularity and centrality to fully connected and weighted complex networks, describe the detection of degenerate high-modularity partitions of these networks, and introduce a weighted-connectivity null model of these networks. We illustrate our methods by demonstrating degenerate high-modularity partitions and strong correlations between two complementary measures of centrality in resting-state functional magnetic resonance imaging (MRI) networks from the 1000 Functional Connectomes Project, an open-access repository of resting-state functional MRI datasets. Our methods may allow more sound and reliable characterizations and comparisons of functional brain networks across conditions and subjects. ► Modularity and centrality in functional brain networks with negative weights. ► Degenerate high-modularity partitions of functional brain networks. ► Weighted null model of functional brain networks.

•New methods to test statistical redundancy of network and gradient structure in fMRI data.•Unbiased and efficient generation of timeseries with network or gradient constraints.•Strong dependence between network and gradient structure in fMRI data.•Networks and gradients are considerably redundant representations of fMRI data. Many studies in human neuroscience seek to understand the structure of brain networks and gradients. Few studies, however, have tested the redundancy between these outwardly distinct features. Here, we developed methods to directly enable such tests. We built on insights from linear algebra to develop methods for unbiased and efficient sampling of timeseries with network or gradient constraints. We used these methods to show considerable redundancy between popular definitions of network and gradient structure in functional MRI data. On the one hand, we found that network constraints largely accounted for the structure of three major gradients. On the other hand, we found that gradient constraints largely accounted for the structure of seven major networks. Our results imply that some networks and gradients may denote discrete and continuous representations of the same aspects of functional MRI data. We suggest that integrated explanations can reduce redundancy by avoiding the attribution of independent existence or function to these features.

Brain connectomes are topologically complex systems, anatomically embedded in 3D space. Anatomical conservation of “wiring cost” explains many but not all aspects of these networks. Here, we examined the relationship between topology and wiring cost in the mouse connectome by using data from 461 systematically acquired anterograde- tracer injections into the right cortical and subcortical regions of the mouse brain. We estimated brain-wide weights, distances, and wiring costs of axonal projections and performed a multiscale topological and spatial analysis of the resulting weighted and directed mouse brain connectome. Our analysis showed that the mouse connectome has small-world properties, a hierarchical modular structure, and greater-than-minimalwiring costs. High-participation hubs of this connectome mediated communication between functionally specialized and anatomically localized modules, had especially high wiring costs, and closely corresponded to regions of the default mode network. Analyses of independently acquired histological and geneexpression data showed that nodal participation colocalized with low neuronal density and high expression of genes enriched for cognition, learning and memory, and behavior. The mouse connectome contains high-participation hubs, which are not explained by wiring-cost minimization but instead reflect competitive selection pressures for integrated network topology as a basis for higher cognitive and behavioral functions.

Self-organized criticality refers to the spontaneous emergence of self-similar dynamics in complex systems poised between order and randomness. The presence of self-organized critical dynamics in the brain is theoretically appealing and is supported by recent neurophysiological studies. Despite this, the neurobiological determinants of these dynamics have not been previously sought. Here, we systematically examined the influence of such determinants in hierarchically modular networks of leaky integrate-and-fire neurons with spike-timing-dependent synaptic plasticity and axonal conduction delays. We characterized emergent dynamics in our networks by distributions of active neuronal ensemble modules (neuronal avalanches) and rigorously assessed these distributions for power-law scaling. We found that spike-timing-dependent synaptic plasticity enabled a rapid phase transition from random subcritical dynamics to ordered supercritical dynamics. Importantly, modular connectivity and low wiring cost broadened this transition, and enabled a regime indicative of self-organized criticality. The regime only occurred when modular connectivity, low wiring cost and synaptic plasticity were simultaneously present, and the regime was most evident when between-module connection density scaled as a power-law. The regime was robust to variations in other neurobiologically relevant parameters and favored systems with low external drive and strong internal interactions. Increases in system size and connectivity facilitated internal interactions, permitting reductions in external drive and facilitating convergence of postsynaptic-response magnitude and synaptic-plasticity learning rate parameter values towards neurobiologically realistic levels. We hence infer a novel association between self-organized critical neuronal dynamics and several neurobiologically realistic features of structural connectivity. The central role of these features in our model may reflect their importance for neuronal information processing.

Background Brain structure and dynamics are interdependent through processes such as activity-dependent neuroplasticity. In this study, we aim to theoretically examine this interdependence in a model of spontaneous cortical activity. To this end, we simulate spontaneous brain dynamics on structural connectivity networks, using coupled nonlinear maps. On slow time scales structural connectivity is gradually adjusted towards the resulting functional patterns via an unsupervised, activity-dependent rewiring rule. The present model has been previously shown to generate cortical-like, modular small-world structural topology from initially random connectivity. We provide further biophysical justification for this model and quantitatively characterize the relationship between structure, function and dynamics that accompanies the ensuing self-organization. Results We show that coupled chaotic dynamics generate ordered and modular functional patterns, even on a random underlying structural connectivity. Consequently, structural connectivity becomes more modular as it rewires towards these functional patterns. Functional networks reflect the underlying structural networks on slow time scales, but significantly less so on faster time scales. In spite of ordered functional topology, structural networks remain robustly interconnected – and therefore small-world – due to the presence of central, inter-modular hub nodes. The noisy dynamics of these hubs enable them to persist despite ongoing rewiring and despite their comparative absence in functional networks. Conclusion Our results outline a theoretical mechanism by which brain dynamics may facilitate neuroanatomical self-organization. We find time scale dependent differences between structural and functional networks. These differences are likely to arise from the distinct dynamics of central structural nodes.

Network analysis can help uncover meaningful regularities in the organization of complex systems. Among these, rich clubs are a functionally important property of a variety of social, technological and biological networks. Rich clubs emerge when nodes that are somehow prominent or ‘rich’ (e.g., highly connected) interact preferentially with one another. The identification of rich clubs is non-trivial, especially in weighted networks and to this end multiple distinct metrics have been proposed. Here we describe a unifying framework for detecting rich clubs which intuitively generalizes various metrics into a single integrated method. This generalization rests upon the explicit incorporation of randomized control networks into the measurement process. We apply this framework to real-life examples and show that, depending on the selection of randomized controls, different kinds of rich-club structures can be detected, such as topological and weighted rich clubs.

Whether unique to humans or not, consciousness is a central aspect of our experience of the world. The neural fingerprint of this experience, however, remains one of the least understood aspects of the human brain. In this paper we employ graph-theoretic measures and support vector machine classification to assess, in 12 healthy volunteers, the dynamic reconfiguration of functional connectivity during wakefulness, propofol-induced sedation and loss of consciousness, and the recovery of wakefulness. Our main findings, based on resting-state fMRI, are three-fold. First, we find that propofol-induced anesthesia does not bear differently on long-range versus short-range connections. Second, our multi-stage design dissociated an initial phase of thalamo-cortical and cortico-cortical hyperconnectivity, present during sedation, from a phase of cortico-cortical hypoconnectivity, apparent during loss of consciousness. Finally, we show that while clustering is increased during loss of consciousness, as recently suggested, it also remains significantly elevated during wakefulness recovery. Conversely, the characteristic path length of brain networks (i.e., the average functional distance between any two regions of the brain) appears significantly increased only during loss of consciousness, marking a decrease of global information-processing efficiency uniquely associated with unconsciousness. These findings suggest that propofol-induced loss of consciousness is mainly tied to cortico-cortical and not thalamo-cortical mechanisms, and that decreased efficiency of information flow is the main feature differentiating the conscious from the unconscious brain.

An understanding of human brain individuality requires the integration of data on brain organization across people and brain regions, molecular and systems scales, as well as healthy and clinical states. Here, we help advance this understanding by leveraging methods from computational genomics to integrate large-scale genomic, transcriptomic, neuroimaging, and electronic-health record data sets. We estimated genetically regulated gene expression (gr-expression) of 18,647 genes, across 10 cortical and subcortical regions of 45,549 people from the UK Biobank. First, we showed that patterns of estimated gr-expression reflect known genetic–ancestry relationships, regional identities, as well as inter-regional correlation structure of directly assayed gene expression. Second, we performed transcriptome-wide association studies (TWAS) to discover 1,065 associations between individual variation in gr-expression and gray-matter volumes across people and brain regions. We benchmarked these associations against results from genome-wide association studies (GWAS) of the same sample and found hundreds of novel associations relative to these GWAS. Third, we integrated our results with clinical associations of gr-expression from the Vanderbilt Biobank. This integration allowed us to link genes, via gr-expression, to neuroimaging and clinical phenotypes. Fourth, we identified associations of polygenic gr-expression with structural and functional MRI phenotypes in the Human Connectome Project (HCP), a small neuroimaging-genomic data set with high-quality functional imaging data. Finally, we showed that estimates of gr-expression and magnitudes of TWAS were generally replicable and that the p -values of TWAS were replicable in large samples. Collectively, our results provide a powerful new resource for integrating gr-expression with population genetics of brain organization and disease.